They are perfectly safe, just like every other commercial airline in the US. With any Google searching, you'll find safety complaints on any airline. I wouldn't make a decision on booking a flight based on safety concerns.

You have a significantly higher chance of being injured/killed with any other mode of transportation in the US. As per a Northwestern University study, "Excluding acts of suicide and terrorism, commercial aviation was the safest mode of travel in the United States, with 0.07 fatalities per billion passenger miles: 'A person who took a 500-mile flight every single day for a year, would have a fatality risk of 1 in 85,000.' "